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We consider a massless and minimally coupled self interacting quantum scalar field in the inflationary de Sitter spacetime. The scalar potential is taken to be a hybrid of cubic and quartic self interactions, V (ϕ) = λ ϕ 4 / 4 ! + β ϕ 3 / 3 ! ( λ > 0 ). Compared to the earlier well studied β = 0 case, the present potential has a rolling down effect due to the ϕ 3 term, along with the usual bounding effect due to the ϕ 4 term. We begin by constructing the Schwinger–Dyson equation for the scalar Feynman propagator up to two loop, at O (λ) , O (β 2) , O (λ 2) and O (λ β 2) . Using this equation, we consider first the local part of the scalar self energy and compute the rest mass squared of the scalar field, dynamically generated via the late time non-perturbative secular logarithms, by resumming the daisy-like graphs. The logarithms associated here are sub-leading, compared to those associated with the non-local, leading terms. We also argue that unlike the quartic case, considering merely the one loop results for the purpose of resummation does not give us any sensible result here. We next construct the non-perturbative two particle irreducible effective action up to three loop and derive from it the Schwinger–Dyson equation once again. This equation is satisfied by the non-perturbative Feynman propagator. By series expanding this propagator, the resummed local part of the self energy is shown to yield the same dynamical mass as that of the above. We next use this equation to resum the effect of the non-local part of the scalar self energy in the Feynman propagator, and show that even though the perturbatively corrected propagator shows secular growth at late times, there exists one resummed solution which is vanishing for large spacelike separations, in qualitative agreement with the well known result found via the stochastic formalism. [ABSTRACT FROM AUTHOR]

The null-surface formulation (NSF) of general relativity differs markedly from the conventional approach. The conventional approach to general relativity is concerned with local fields such as the metric, whereas the NSF focuses on surfaces. The NSF has two distinct but mathematically equivalent interpretations: (a) Future-directed light rays leave a spacetime point and intersect future null-infinity. The resulting surface, known as a light-cone cut, encodes the properties of the spacetime; (b) The angular coordinates (Bondi coordinates) of null-infinity are used to label past light cones, thereby producing a family of null surfaces. These will satisfy the NSF field equations and a solution of these equations provides a description of spacetime. This paper features a new exact solution that, for the first time, directly links the two interpretations, thereby illustrating both approaches and demonstrating their equivalence. The solution and its properties are first explored in 2+1 dimensions, after which, the generalization to 3+1 is outlined. [ABSTRACT FROM AUTHOR]

We study a model of the neutron star in κ -deformed space-time in the presence of the cosmological constant (Λ ). The Einstein tensor and the energy-momentum tensor are generalized to κ -deformed space-time and we construct the field equations with the cosmological constant. Considering the interior of the star to be a perfect fluid as in the commutative case, we find the Tolman–Oppenheimer–Volkoff equations with the inclusion of the cosmological constant in κ -deformed space-time. The behavior of the maximum allowed mass of the star and its radius are studied with the variation in the cosmological constant as well as the deformation parameter. We see that the non-commutativity enhances the mass of the star and its maximum mass increases with a decrease in the cosmological constant. The maximum mass varies from 3.44 to 3.68 M ⊙ as Λ varies from 10 - 10 to 10 - 15 m - 2 . We also obtain the compactness factor and surface redshift of the star. We observe that the compactness of the star increases as the cosmological constant decreases, whereas the surface redshift of the star decreases with a decrease in the cosmological constant. The compactness factor and surface redshift corresponding to the maximum mass of the neutron star remains almost constant as Λ decreases. [ABSTRACT FROM AUTHOR]

In this paper we use the Homotopy analysis method to obtain an analytic approximation for the entire photon trajectory in the Schwarzschild spacetime. This is usually expressed exactly in terms of an elliptic integral. We compare our approximation with other formulae found in the literature, which were specifically obtained for the Schwarzschild solution. Unlike some of these formulae, our approximation can be applied and maintains a good accuracy for emission point close to the event horizon and also for emission angles close to and greater than π / 2 . We show that our method can easily be applied to other spherically symmetric solutions such as the Reissner-Nordström solution. Such an approximation would be useful when accurate determination of the light trajectories around compact objects is required without the need to revert to time consuming numerical integration of elliptic integrals. [ABSTRACT FROM AUTHOR]

The center-of-mass energy of two colliding particles could be arbitrarily high in the vicinity of event horizons of the extremal Myers-Perry black holes if the angular momentum of colliding particles is fine-tuned to the critical values. We investigate the maximum efficiency of two colliding particles in four and six dimensions. The efficiency of collision for two particles near the four-dimensional Kerr black holes is 130%. We show that the efficiency increases to 145% for collision in six dimensions. We also show that the region for the polar angle in which the particle can reach the high energy is larger when the dimension of space-time increases. [ABSTRACT FROM AUTHOR]

Beginning from the standard Arnowitt–Deser–Misner (ADM) formulation of general relativity we construct a tentative model of quantum gravity from the point of view of an observer with constant proper acceleration, just outside of a horizon of spacetime. In addition of producing the standard results of black-hole thermodynamics, our model makes an entirely new prediction that there is a certain upper bound for the energies of massive particles. For protons, for instance, this upper bound is around 1.1 × 10 21 eV. The result is interesting, because this energy is roughly of the same order of magnitude as are the highest energies ever measured for protons in cosmic rays. [ABSTRACT FROM AUTHOR]

We investigate the turnaround radius of the Reissner–Nordström deSitter Spacetime and how the turnaround radius changes if a test particle carries charge. We also consider the Martínez–Troncoso–Zanelli (MTZ) solution of conformally coupled gravity and investigate how the turnaround radius changes for a scalar test charge. In both scalar and electric interaction cases we find that the Turnaround Radius depends on the particle's energy. [ABSTRACT FROM AUTHOR]

The process of the gravitational collapse might lead not only to a black hole but also to naked singularity formation. In this paper, we consider the generalized Vaidya spacetime with polytropic and generalized polytropic equations of state. We solve the Einstein and Einstein–Maxwell equations to obtain the explicit form of a mass function. We consider the limiting cases of solutions and find out, that generalized Vaidya spacetime might behave like Vaidya–de Sitter and Bonnor–Vaidya–de sitter solutions. Moreover, we explicitly show, that the part of solution, which depends on the polytropic index, is similar to cosmological fields surrounding both Vaidya and Bonnor–Vaidya black holes. The process of the gravitational collapse has been then considered. We have found out that the conditions of the naked singularity formation don't depend on the polytropic index. [ABSTRACT FROM AUTHOR]

We study the higher dimensional scenario of an anisotropic compact star using the Buchdahl–Vaidya–Tikekar metric ansatz. In our formalism, the anisotropy is assumed in such a way that, in the absence of it, the solution reduces to Schwarzschild's interior solution in D ≥ 4 dimensions. The model is so developed that it correlates anisotropy to the curvature parameter K which characterizes a departure from spherical geometry of the t = constant hypersurface of the associated spacetime when embedded in a 4 dimensional Euclidean space. Due to the particular choice of anisotropy, the pressure balancing equation for hydrostatic equilibrium continues to have the same form in higher dimensions. Consequently, our approach permits extending a four-dimensional solution to a higher dimensional spacetime without deforming the sphericity of the configuration. Making use of the model, we propose a higher dimensional anisotropic analogue of the Buchdahl bound on compactness. We show that additional dimension as well as anisotropy reduce the compactification limit. Our technique helps to regain the original Buchdahl limit in D = 4 dimensions and also, in the absence of anisotropy, the compactification limit in higher dimensions obtained earlier by Leon and Cruz (Gen Relativ Gravit 32:1207–1216, 2000. https://doi.org/10.1023/A:1001982402392). It turns out that the maximum achievable dimension remains model dependent through the causality condition and the compactification limit. We scrutinize the model under all the requisite physical conditions for a relativistic anisotropic fluid sphere which might serve as the internal structure of a compact star in higher dimensions. We analyze the consequences of the departure from homogeneous spherical distribution and dimensionality on the physical behaviour of the star. The EOS becomes stiffer in higher dimensions and comparatively lower anisotropic stress. Our calculation shows that the central density reduces as we move towards higher dimensions and inclusion of anisotropy increases the rate of fall of the density profile. We also note that the two pressures get reduced considerably in higher dimensions. We show that, for a given curvature parameter specifying the sphericity, an extra dimension is analogous to moving towards a homogeneous distribution of an anisotropic star. [ABSTRACT FROM AUTHOR]

The analysis of the continual gravitational contraction of a spherically symmetric shell of charged radiation is extended to higher dimensions in Einstein–Gauss–Bonnet gravity. The spacetime metric, which is of Boulware–Deser type, is real only up to a maximum electric charge and thus collapse terminates with the formation of a branch singularity. This branch singularity divides the higher dimensional spacetime into two regions, a real and physical one, and a complex region. This is not the case in neutral Einstein–Gauss–Bonnet gravity as well as general relativity. The charged gravitational collapse process is also similar for all dimensions N ≥ 5 unlike in the neutral scenario where there is a marked difference between the N = 5 and N > 5 cases. In the case where N = 5 uncharged collapse ceases with the formation of a weaker, conical singularity which remains naked for a time depending on the Gauss–Bonnet invariant, before succumbing to an event horizon. The similarity of charged collapse for all higher dimensions is a unique feature in the theory. The sufficient conditions for the formation of a naked singularity are studied for the higher dimensional charged Boulware–Deser spacetime. For particular choices of the mass and charge functions, naked branch singularities are guaranteed and indeed inevitable in higher dimensional Einstein–Gauss–Bonnet gravity. The strength of the naked branch singularities is also tested and it is found that these singularities become stronger with increasing dimension, and no extension of spacetime through them is possible. [ABSTRACT FROM AUTHOR]

We study the renormalized stress-energy tensor (RSET) for a massless, conformally coupled scalar field on global anti-de Sitter space-time in four dimensions. Robin (mixed) boundary conditions are applied to the scalar field. We compute both the vacuum and thermal expectation values of the RSET. The vacuum RSET is a multiple of the space-time metric when either Dirichlet or Neumann boundary conditions are applied. Imposing Robin boundary conditions breaks the maximal symmetry of the vacuum state and results in an RSET whose components with mixed indices have their maximum (or maximum magnitude) at the space-time origin. The value of this maximum depends on the boundary conditions. We find similar behaviour for thermal states. As the temperature decreases, thermal expectation values of the RSET approach those for vacuum states and their values depend strongly on the boundary conditions. As the temperature increases, the values of the RSET components tend to profiles which are the same for all boundary conditions. We also find, for both vacuum and thermal states, that the RSET on the space-time boundary is independent of the boundary conditions and determined entirely by the trace anomaly. [ABSTRACT FROM AUTHOR]

Starting from a general transformation for spherically symmetric metrics where g_11=-1/g_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one where tortoise coordinate appears as the unique solution, other that includes Kruskal-Szekeres coordinates as a very specific case, but that also allows other similar transformations, and finally a new set of coordinates with very different properties than the other two. In particular, it represents any causal patch of the spherically symmetric metrics in a compactified form. We analyze general properties of the new proposed "pulsating coordinates", and then proceed to apply the transformation for the Schwarzschild spacetime, as well as for several cosmological solutions, contrasting properties with the Kruskal case. In particular, Anti-de-Sitter solution presents interesting features. [ABSTRACT FROM AUTHOR]

Let M be a locally rotationally symmetric spacetime, and ξ a a conformal Killing vector for the metric on M, lying in the subspace spanned by the unit timelike direction and the preferred spatial direction, and with non-constant components. Under the assumption that the divergence of ξ a has no critical point in M, we obtain the necessary and sufficient condition for ξ a to generate a conformal Killing horizon. It is shown that ξ a generates a conformal Killing horizon if and only if either of the components (which coincide on the horizon) is constant along its orbits. That is, a conformal Killing horizon can be realized as the set of critical points of the variation of the component(s) of the conformal Killing vector along its orbits. Using this result, a simple mechanism is provided by which to determine if an arbitrary vector in an expanding LRS spacetime is a conformal Killing vector that generates a conformal Killing horizon. In specializing the case for which ξ a is a special conformal Killing vector, provided that the gradient of the divergence of ξ a is non-null, it is shown that LRS spacetimes cannot admit a special conformal Killing vector field, thereby ruling out conformal Killing horizons generated by such vector fields. [ABSTRACT FROM AUTHOR]

In this paper we study the global existence and completeness of classical solutions of gravity coupled a scalar field system called Einstein–Klein–Gordon system in higher dimensions. We introduce a new ansatz function to reduce the problem into a single first-order integro-differential equation. Then, we employ the contraction mapping in the appropriate Banach space. Using Banach fixed theorem, we show that there exists a unique fixed point, which is the solution of the theory. For a given initial data, we prove the existence of both local and global classical solutions. We also study the completeness properties of the spacetime. Here, we introduce a mass-like function for D ≥ 4 in Bondi coordinates. The completeness of spacetime along the future directed timelike lines outward to a region which resembles the event horizon of the black hole. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the relativistic and nonrelativistic energy spectra (fermionic Landau levels) for the noncommutative quantum Hall effect with anomalous magnetic moment in the conical Gödel-type spacetime in (2 + 1) -dimensions, where such spacetime is the combination of the flat Gödel-type spacetime with a cosmic string (conical gravitational topological defect). To analyze these energy spectra, we start from the noncommutative Dirac equation with minimal and nonminimal couplings in polar coordinates. Using the tetrads formalism, we obtain a second-order differential equation. Next, we solve exactly this differential equation, where we obtain a generalized Laguerre equation, and also a quadratic polynomial equation for the total relativistic energy. By solving this polynomial equation, we obtain the relativistic energy spectrum of the fermion and antifermion. Besides, we also analyze the nonrelativistic limit of the system, where we obtain the nonrelativistic energy spectrum. In both cases (relativistic and nonrelativistic), we discuss in detail the characteristics of each spectrum as well as the influence of all parameters and physical quantities in such spectra. Comparing our problem with other works, we verified that our results generalize several particular cases in the literature. [ABSTRACT FROM AUTHOR]

The present paper focused on Vaidya spacetime admitting a conformal Ricci soliton. We derive the expressions for the four components of the associated vector field V and demonstrate that, under this condition, the spacetime reduces to the Schwarzschild spacetime. Furthermore, we determine the necessary expression for the potential function f to establish the existence of a conformal gradient Ricci soliton in the Vaidya spacetime and we provide the condition for which the soliton is shrinking, steady or expanding. [ABSTRACT FROM AUTHOR]

Wormholes, theoretical structures that connect disparate regions of spacetime, present intriguing possibilities for interstellar travel and exploitation. By the technique of differential forms, we have obtained Ricci rotation coefficients. The Lanczos potential is derived from the Weyl–Lanczos equations and general observer quantities. Also, through analytical calculations, we quantify the influence of the Lanczos potential on various physical quantities, such as tidal forces and shape function at the throat of the wormhole. [ABSTRACT FROM AUTHOR]

External non-minimally coupled scalar and spinor field perturbations have been studied in a (1 + 1) dimensional dilatonic blackhole spacetime (Mandal et al. in Mod Phys Lett A 6:1685–1692. https://doi.org/10.1142/S0217732391001822, 1991; Witten in Phys Rev D 44:314–324. https://doi.org/10.1103/PhysRevD.44.314, 1991). Exact analytical expressions of the quasi-normal mode frequencies have been found for both the cases. In the scalar perturbations the quasi-normal mode frequencies turn out to be purely imaginary and negative. Furthermore we have found that the quasi-normal frequencies for Dirac field exhibit both real and imaginary part. The QNM frequencies decay monotonically with the overtone number under certain class of the blackhole parameters. The decay profile ensures the stability of the blackhole spacetime under these perturbations. [ABSTRACT FROM AUTHOR]

In the Alcubierre warp-drive spacetime, we investigate the following scalar curvature invariants: the scalar I, derived from a quadratic contraction of the Weyl tensor, the trace R of the Ricci tensor, and the quadratic r1 and cubic r2 invariants from the trace-adjusted Ricci tensor. In four-dimensional spacetime the trace-adjusted Einstein and Ricci tensors are identical, and their unadjusted traces are oppositely signed yet equal in absolute value. This allows us to express these Ricci invariants using Einstein's curvature tensor, facilitating a direct interpretation of the energy-momentum tensor. We present detailed plots illustrating the distribution of these invariants. Our findings underscore the requirement for four distinct layers of an anisotropic stress-energy tensor to create the warp bubble. Additionally, we delve into the Kretschmann quadratic invariant decomposition. We provide a critical analysis of the work by Mattingly et al., particularly their underrepresentation of curvature invariants in their plots by 8 to 16 orders of magnitude. A comparison is made between the spacetime curvature of the Alcubierre warp-drive and that of a Schwarzschild black hole with a mass equivalent to the planet Saturn. The paper addresses potential misconceptions about the Alcubierre warp-drive due to inaccuracies in representing spacetime curvature changes and clarifies the classification of the Alcubierre spacetime, emphasizing its distinction from class B warped product spacetimes. [ABSTRACT FROM AUTHOR]

Motivated by the nonextensive nature of entropy in the gravitational context and the Gauge/Gravity duality, black hole thermodynamics has been attracting intense emphasis in the literature. Along the present work, we investigate some features of the phase structure and critical phenomena of the 4-dimensional charged black holes in asymptotically flat spacetime within the formalism of Rényi statistics. First, we explore the extended phase space via the Rényi statistics approach. Concretely, based on the modified version of the Smarr formula, we recall the equal-area law to remove the oscillatory non-physical region in the P R - V and T R - S R planes. Then, the coexistence curves are determined, as well as the latent heat of phase change. Moreover, we prove that the critical exponent describing the behavior of the order parameter near the critical point is 1 2 , which is consistent with Landau's theory of continuous phase transition. Lastly, we apply the Hamiltonian approach to Rényi thermodynamics which provides a new and solid mathematical basis for the extension of phase space and puts more insight into an expected and profound possible connection between the nonextensivity Rényi parameter λ and the cosmological constant Λ . [ABSTRACT FROM AUTHOR]

Regular black holes are often geodesically incomplete when their extensions to negative values of the radial coordinate are considered. Here, we propose to use the Simpson–Visser method of regularising a singular spacetime, and apply it to a regular solution that is geodesically incomplete, to construct a geodesically complete regular solution. Our method is generic, and can be used to cure geodesic incompleteness in any spherically symmetric static regular solution, so that the resulting solution is symmetric in the radial coordinate. As an example, we illustrate this procedure using a regular black hole solution with an asymptotic Minkowski core. We study the structure of the resulting metric, and show that it can represent a wormhole or a regular black hole with a single or double horizon per side of the throat. Further, we construct a source Lagrangian for which the geodesically complete spacetime is an exact solution of the Einstein equations, and show that this consists of a phantom scalar field and a nonlinear electromagnetic field. Finally, gravitational lensing properties of the geodesically complete spacetime are briefly studied. [ABSTRACT FROM AUTHOR]

What is the analogous notion of Gromov–Hausdorff convergence for sequences of spacetimes? Since a Lorentzian manifold is not inherently a metric space, one cannot simply use the traditional definition. One approach offered by Sormani and Vega (Class Quant Gravity, 33:085001, 2016) is to define a metric space structure on a spacetime by means of the null distance. Then one can define convergence of spacetimes using the usual definition of Gromov–Hausdorff convergence. In this paper we explore this approach by giving many examples of sequences of warped product spacetimes with the null distance converging in the Gromov–Hausdorff sense. In addition, we give an optimal convergence theorem which shows that under natural geometric hypotheses a sequence of warped product spacetimes converge to a specific limiting warped product spacetime. The examples given further serve to show that the hypotheses of this convergence theorem are optimal. [ABSTRACT FROM AUTHOR]

We present the second post-Newtonian solution for the quasi-Keplerian motion of a test particle in the gravitational field of Bardeen black hole. This solution is formulated in terms of energy and angular momentum of the particle, as well as the black hole's magnetic charge. The leading effects of the magnetic charge on the test particle's orbit and motion including perihelion precession are displayed explicitly. In particular, it is shown that the magnetic charge does not have effects on the orbital period when the second post-Newtonian order is considered. [ABSTRACT FROM AUTHOR]

In this study, we present a novel solution in Einstein–Maxwell theory that represents the magnetized Taub–NUT spacetime incorporating the Manko–Ruiz parameter. We investigate various aspects of this spacetime, including its curvature, closed timelike curve, and electromagnetic fields. Additionally, we explore the phenomenon of Hawking radiation within this magnetized spacetime by employing the tunneling picture. Our findings shed light on the unique characteristics and physical implications of the magnetized Taub–NUT spacetime with the Manko–Ruiz parameter. [ABSTRACT FROM AUTHOR]

Through the Ernst formalism we provide expression for a class of colliding Einstein-Maxwell (EM) metrics with cross polarization. Local isometry is imposed as a means to transform interaction region of the spacetime into stationary, charged Zipoy–Voorhees (ZV) metric in Schwarzschild coordinates. This is known as the Chandrasekhar-Xanthopoulos (CX) duality which maps the plane of double-null coordinates (with two spacelike cyclic coordinates) to the static/stationary spacetime. The ZV-metric is known to describe planetary/stellar objects with arbitrary distortion parameter. Asymptotic behaviour of the metric for practical use is provided. "The world may be seen in a grain of sand" - William Blake. [ABSTRACT FROM AUTHOR]

The non-trivial naked singularities that possess directional behavior in the charged and uncharged Zipoy-Voorhees (ZV) spacetimes, known as γ - m e t r i c s are investigated within the context of quantum mechanics. Classically singular spacetime is understood as a geodesic incompleteness with respect to a particle probe, while quantum singularity is understood as a non-unique evolution of test quantum wave packets. In this study, quantum wave packets obeying Klein–Gordon equation are used to probe timelike naked singularities. It is shown by rigorous mathematical calculations that the outermost singularity developed in the charged and uncharged ZV spacetime on the equatorial plane is quantum mechanically singular for all values of the deformation parameter γ . However, directional singularities that develop on the symmetry axis is shown to be healed partially for specific range of the parameter γ , if the analysis is restricted purposely to only specific mode (s-wave mode). Allowing arbitrary modes, classical directional singularities remains quantum singular. [ABSTRACT FROM AUTHOR]

Dissipative force–flux relations are established in a strict covariant fashion for a relativistic fluid in a general curved space–time within the framework of kinetic theory. The Boltzmann equation is addressed to first order in the gradients by employing the Chapman–Enskog expansion and the corresponding constitutive equations are derived by considering a relaxation approximation. It is shown that in the heat flux, only the corresponding transport coefficient is modified when the gradients of the state variables are considered as the thermodynamic forces. On the other hand, the viscous terms features new driving terms due to the curvature of space–time that only vanish in particular cases. [ABSTRACT FROM AUTHOR]

The present paper is devoted to analyzing light deflection caused by the presence of a cosmological constant in a space-time described by the Szekeres–Szafron metric. We use the orbital equation for light to calculate the deflection angle in gravitational lensing in the equatorial plane of the Szekeres–Szafron metric. The present study confirms that the cosmological constant has an effect on gravitational lensing. [ABSTRACT FROM AUTHOR]

We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate r between two values r 1 and r 2 . The solution is given in three regions, one being the well-known analytical Schwarzschild solution in the outer vacuum region, one being determined analytically in the inner vacuum region, and one being determined mostly analytically but partially numerically, within the matter region. The solutions for the temporal coefficient of the metric and for the pressure within this region are given in terms of a non-elementary but fairly straightforward real integral. For some values of the parameters this integral can be written in terms of elementary functions. We show that in this solution there is a singularity at the origin, and give the parameters of that singularity in terms of the geometrical and physical parameters of the shell. This does not correspond to an infinite concentration of matter, but in fact to zero energy density at the center. It does, however, imply that the spacetime within the spherical cavity is not flat, so that there is a non-trivial gravitational field there, in contrast with Newtonian gravitation. This gravitational field is repulsive with respect to the origin, and thus has the effect of stabilizing the geometrical configuration of the matter, since any particle of the matter that wanders out into either one of the vacuum regions tends to be brought back to the bulk of the matter by the gravitational field. [ABSTRACT FROM AUTHOR]

In quadratic gravity, the junction conditions are six in number and permit the appearance of double layer thin shells. Double layers arise typically in theories with dipoles, i.e., two opposite charges, such as electromagnetic theories, and appear exceptionally in gravitational theories, which are theories with a single charge. We explore this property of the existence of double layers in quadratic gravity to find and study traversable wormholes in which the two domains of the wormhole interior region, where the throat is located, are matched to two vacuum domains of the exterior region via the use of two double layer thin shells. The quadratic gravity we use is essentially given by a R + α R 2 Lagrangian, where R is the Ricci scalar of the spacetime and α is a coupling constant, plus a matter Lagrangian. The null energy condition, or NEC for short, is tested for the whole wormhole spacetime. The analysis shows that the NEC is satisfied for the stress-energy tensor of the matter in the whole wormhole interior region, notably at the throat, and is satisfied for some of the stress–energy tensor components of the matter at the double layer thin shell, but is not satisfied for some other components, namely, the double layer stress–energy distribution component, at the thin shell. This seems to mean that the NEC is basically impossible, or at least very hard, to be satisfied when double layer thin shells are present. Single layer thin shells are also admitted within the theory, and we present thin shell traversable wormholes, i.e., wormholes without interior, with a single layer thin shell at the throat for which the corresponding stress–energy tensor satisfies the NEC, that are asymmetric, i.e., with two different vacuum domains of the exterior region joined at the wormhole throat. [ABSTRACT FROM AUTHOR]

We study the geometric properties of certain Codazzi tensors for their own sake, and for their appearance in the recent theory of Cotton gravity. We prove that a perfect-fluid tensor is Codazzi if and only if the metric is a generalized Stephani universe. A trace condition restricts it to a warped space-time, as proven by Merton and Derdziński. We also give necessary and sufficient conditions for a space-time to host a current-flow Codazzi tensor. In particular, we study the static and spherically symmetric cases, which include the Nariai and Bertotti-Robinson metrics. The latter are a special case of Yang Pure space-times, together with spatially flat FRW space-times with constant curvature scalar. We apply these results to the recent Cotton gravity by Harada. We show that the equation of Cotton gravity is Einstein's equation modified by the presence of a Codazzi tensor, which can be chosen freely and constrains the space-time where the theory is staged. In doing so, the tensor (chosen in forms appropriate for physics) implies the form of the Ricci tensor. The two tensors specify the energy-momentum tensor, which is the source in the equation of Cotton gravity for the metric implied by the Codazzi tensor. For example, we show that the Stephani, Nariai and Bertotti-Robinson space-times are characterized by a "current flow" Codazzi tensor. Because of it, they solve Cotton gravity with physically sensible energy-momentum tensors. Finally, we discuss Cotton gravity in constant curvature space-times. [ABSTRACT FROM AUTHOR]

Milne-like spacetimes are a class of hyperboloidal FLRW spacetimes which admit continuous spacetime extensions through the big bang, τ = 0 . In a previous paper [27], it was advocated that the existence of this big bang extension could have applications to fundamental problems in cosmology, which illustrates the physical importance of such extensions. By definition, the scale factor for a Milne-like spacetime satisfies the past asymptotic assumption a (τ) = τ + o (τ 1 + ε) as τ → 0 for some ε > 0 . The existence of the big bang extension follows from writing the metric in conformal Minkowskian coordinates and using the past asymptotic assumption of the scale factor. This asymptotic assumption implies a (τ) = τ + o (τ) as τ → 0 . In this paper, we show that a (τ) = τ + o (τ) is not sufficient to achieve a big bang extension, but it is necessary (provided its derivative converges as τ → 0 ). We also show that the ε in a (τ) = τ + o (τ 1 + ε) is not necessary to achieve a big bang extension. [ABSTRACT FROM AUTHOR]

In this paper we present a space-time calculus for symmetric spinors, including a product with a number of index contractions followed by symmetrization. As all operations stay within the class of symmetric spinors, no involved index manipulations are needed. In fact spinor indices are not needed in the formalism. It is also general because any covariant tensor expression in a 4-dimensional Lorentzian spacetime can be translated to this formalism. The computer algebra implementation SymSpin as part of xAct for Mathematica is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we solved the Einstein's field equation and obtained a line element for static, ellipsoidal objects characterized by the linear eccentricity (η ) instead of quadrupole parameter (q). This line element recovers the Schwarzschild line element when η is zero. In addition to that it also reduces to the Schwarzschild line element, if we neglect terms of the order of r - 2 or higher which are present within the expressions for metric elements for large distances. Furthermore, as the ellipsoidal character of the derived line element is maintained by the linear eccentricity (η ), which is an easily measurable parameter, this line element could be more suitable for various analytical as well as observational studies. [ABSTRACT FROM AUTHOR]

In this paper, we prove the global existence of classical static solutions of Einstein's gravitational theory coupled to a real scalar field where spacetime admits spherically symmetry. The equations of motions can then be reduced into a single first-order integro-differential equation. First, we obtain the decay estimates of the solutions. Then, to prove the global existence, we use the contraction mapping theorem in the appropriate function spaces. [ABSTRACT FROM AUTHOR]

We revisit an older concept in singularity theory: that in the presence of the strong energy condition (SEC), a static or stationary spacetime must have a quadratic fall-off in a characteristic Ricci quantity, in order for the spacetime to be without singularities (or, at least, to be both globally hyperbolic and timelike or null geodesically complete). We replace SEC with the null energy condition (NEC), and apply the methods used previously on timelike geodesics, to null geodesics instead. The results are noticeably weaker for the NEC case than for SEC: using a somewhat different characteristic measure of Ricci curvature, we obtain a fall-off which is quadratic only if there is not much asymptotic change in the size of the Killing field: we employ a ratio of maximum size to square of minimum size of the Killing field—within a ball of given radius r—in addition to 1 / r 2 . [ABSTRACT FROM AUTHOR]

What happens when a warp bubble has mass? This seemingly innocent question forces one to carefully formalize exactly what one means by a warp bubble, exactly what one means by having the warp bubble "move" with respect to the fixed stars, and forces one to more carefully examine the notion of mass in warp-drive spacetimes. This is the goal of the present article. In this process, we will see that often-made throw-away comments regarding "payloads" are even simpler than commonly assumed, while there are two further, distinct yet subtle ways in which a mass can appear in connection with a warp drive space-time: One, that the warp bubble (not its payload) has the mass; two, that the mass is a background feature in front of which the warp drive moves. For simplicity, we consider generic Natário warp drives with zero-vorticity flow field. The resulting spacetimes are sufficiently simple to allow an exact and fully explicit computation of all of the stress-energy components, and verify that (as expected) the null energy condition (NEC) is violated. Likewise the weak, strong, and dominant energy conditions (WEC, SEC, DEC) are violated. Indeed, this confirms the community's folk wisdom, and recent (fully general, but implicit) results of the present authors which closed previous gaps in the argument. However, folk wisdom should be carefully and critically examined before being believed, and the present examples for general results will greatly aid physical intuition. [ABSTRACT FROM AUTHOR]

We analyse the evolution of a generalized bosonic oscillator in the near horizon geometry of the BTZ black hole by analytically obtaining a solution of the associated Klein–Gordon equation. We show that it is possible to obtain relativistic frequency expression in closed-form for the system in question. Here, we observe that such a system decays in time without any real oscillation and the damped modes depend explicitly on the parameters of the oscillator coupling besides the parameters of the background geometry. This result allows us to analyse the influences of both oscillator coupling and spacetime parameters on the evolution of such a test field. Also, the results indicate that the spacetime background is stable under this perturbation field. [ABSTRACT FROM AUTHOR]

We study a quantum scalar field, with general mass and coupling to the scalar curvature, propagating on three-dimensional global anti-de Sitter space-time. We determine the vacuum and thermal expectation values of the square of the field, also known as the vacuum polarisation (VP). We consider values of the scalar field mass and coupling for which there is a choice of boundary conditions giving well-posed classical dynamics. We apply Dirichlet, Neumann and Robin (mixed) boundary conditions to the field at the space-time boundary. We find finite values of the VP when the parameter governing the Robin boundary conditions is below a certain critical value. For all couplings, the vacuum expectation values of the VP with either Neumann or Dirichlet boundary conditions are constant and respect the maximal symmetry of the background space-time. However, this is not the case for Robin boundary conditions, when both the vacuum and thermal expectation values depend on the space-time location. At the space-time boundary, we find that both the vacuum and thermal expectation values of the VP with Robin boundary conditions converge to the result when Neumann boundary conditions are applied, except in the case of Dirichlet boundary conditions. [ABSTRACT FROM AUTHOR]

The singularity theorems of Penrose, Hawking, and Geroch predict the existence of incomplete inextendible causal geodesics in a wide range of physically adequate spacetimes modeling the gravitational collapse of stars and the expanding universe. Here, using results on spacetime extensions, it is shown that if a suitable low regular form of the strong cosmic censor hypothesis holds, then parallelly propagated blow-up of either the tidal force or frame-drag part of the curvature must occur in "generic" timelike geodesically incomplete maximal Cauchy developments. [ABSTRACT FROM AUTHOR]

In this article, we analytically investigate the microstructure of a five-dimensional neutral Gauss–Bonnet black hole, in the background of anti-de Sitter spacetime, by using the scalar curvature of the Ruppeiner geometry constructed via adiabatic compressibility. The microstructure details associated with the small-large black hole phase transition are probed in the parameter space of pressure and volume. The curvature scalar shows similar properties for both phases of the black hole, it diverges at the critical point with a critical exponent 2, and approaches zero for extremal black holes. We show that the dominant interaction among black hole molecules is attractive. This study also confirms that the nature of the microstructure interaction remains unchanged during the small-large black hole phase transition, even though the microstructures are different for both phases. [ABSTRACT FROM AUTHOR]

We study new solutions of black-bounce spacetimes formulated in f(T) gravity in four dimensions. First, we present the case of diagonal tetrad where a restriction appears in the equations of motion that is divided into the cases of zero torsion, constant torsion and teleparallel. The Null Energy Condition (NEC) is still always violated, which implies that the other energy conditions are also violated. The solutions are regular throughout spacetime and the zero torsion solution presents discontinuity between the energy conditions inside and outside the event horizon. Second, we present the case of non-diagonal tetrads. This case is divided into a Simpson-Visser type model and a quadratic model in T. The NEC continues to be violated, implying the violation of the other energy conditions. The solutions are regular in all spacetimes. An interesting result is that due to the possibility that the area associated with the metric is different from 4 π r 2 , the no-go output theorem established in the usual f(T) is violated, resulting in the new possibility g 00 = - g 11 , for metric components. [ABSTRACT FROM AUTHOR]

We give an example of a spacetime with a continuous metric which is globally hyperbolic and exhibits causal bubbling. The metric moreover splits orthogonally into a timelike and a spacelike part. We discuss our example in the context of energy conditions and the recently introduced synthetic timelike curvature-dimension (TCD) condition. In particular we observe that the TCD-condition does not, by itself, prevent causal bubbling. [ABSTRACT FROM AUTHOR]

We discuss the tension between the possible existence of Painlevé–Gullstrand coordinate systems versus the explicit geometrical features of the Kerr spacetime; a subject of interest to Professor Thanu Padmanabhan in the weeks immediately preceding his unexpected death. We shall carefully distinguish strong and weak Painlevé–Gullstrand coordinate systems, and conformal variants thereof, cataloguing what we know can and cannot be done—sometimes we can make explicit global statements, sometimes we must resort to implicit local statements. For the Kerr spacetime the best that seems to be achievable is to set the lapse function to unity and represent the spatial slices with a 3-metric in factorized unimodular form; this arises from considering the Doran version of Kerr spacetime in Cartesian coordinates. We finish by exploring the (limited) extent to which this construction might possibly lead to implementing an "analogue spacetime" model suitable for laboratory simulations of the Kerr spacetime. [ABSTRACT FROM AUTHOR]

We identify certain general geometric conditions on a foliation of a spacetime (M, g) by timelike curves that will impede the existence of null geodesic lines, especially if (M, g) possesses a compact Cauchy hypersurface. The absence of such lines, in turn, yields well-known restrictions on the geometry of cosmological spacetimes, in the context of Bartnik's splitting conjecture. Since the (non)existence of null lines is actually a conformally invariant property, such conditions only need to apply for some suitable conformal rescaling of g. [ABSTRACT FROM AUTHOR]

We consider a characteristic initial value problem, with initial data given on a truncated null cone, for the Einstein–Maxwell–Klein–Gordon system with a positive cosmological constant to the Bondi-spherically symmetric spacetime. We prove that, for small initial data, this system has a unique global in (Bondi) time solution which is causally geodesically complete to the future and decay exponentially in (Bondi) time approaching the de Sitter solution. [ABSTRACT FROM AUTHOR]

We introduce a new equation we dubbed the modular Dirac equation to see and reconstruct a spin 1/2 particle at the center of a nearly A d S 2 spacetime in the entanglement wedge reconstruction paradigm and we study hidden symmetries of this spacetime, too. Various properties of the Dirac modular operator are studied: a generalized Tomita–Takesaki construction, the connection to the Schwarzian derivative of the logarithm of the modular Dirac operator, the link with the an allowable complex metric, the connection to regenesis, we write the corresponding Lagrangian of the modular Dirac equation and we put in perspective some limitations of the current bulk reconstruction in the case ofs unknown couplings. [ABSTRACT FROM AUTHOR]

The introduction of extra dimensions is an invaluable strategy for the unification of gravity with other physical fields. Nevertheless, the matter in hand is to be eventually reduced to the actual 4D spacetime. The Kaluza–Klein theory is no exception to this well-known scheme. There are two procedures to obtain the field equations from a higher dimensional action. One can either take the variation of the effective action in that higher dimension and then reduce the resulting equations or reduce the higher dimensional action to the actual 4D and henceforward take the variations with respect to the constituent fields of the theory. Here, for the case of a quadratic curvature model with a Kaluza–Klein ansatz the field equations are obtained from the reduced action and compatibility of these two procedures is discussed in detail. [ABSTRACT FROM AUTHOR]

We discuss spacetime instability for effective field theories of quantum gravity. The effective action of gravity introduces infinite higher derivative curvature terms R 2 , R μ ν R μ ν , R μ ν κ λ R μ ν κ λ ⋯ . Although these higher derivative curvature terms are indispensable to construct the self-consistent renormalizable theory of quantum gravity, they lead to several pathologies. We clearly show that even if they are written as the Planck-suppressed operators they lead to serious consequences and and de Sitter or radiation-dominated Universe is highly unstable. We show that the couplings of these higher derivative curvatures must satisfy a 1 , 2 , 3 ≳ 10 118 to be consistent with the cosmological observations. Thus, the standard effective field theories of quantum gravity fail to describe the observed Universe unless introducing a specific technique dealing with the higher derivative curvature terms. [ABSTRACT FROM AUTHOR]

The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal boundary are surveyed and revisited, starting at the seminal conformal boundary constructions by R. Penrose. Our study covers: (1) adaptive possibilities and techniques for their Cauchy slicings, (2) global hyperbolicity of sliced spacetimes, (3) critical review on the conformal and causal boundaries for a globally hyperbolic spacetime, and (4) procedures to compute the causal boundary of a Cauchy temporal splitting by using isocausal comparison with a static product. New simple counterexamples on R 2 illustrate a variety of possibilities related to these splittings, such as the logical independence (for normalized sliced spacetimes) between the completeness of the slices and global hyperbolicity, the necessity of uniform bounds on the slicings in order to ensure global hyperbolicity, or the insufficience of these bounds for the computation of the causal boundary. A refinement of one of these examples shows that the space of all the (normalized, conformal classes of) globally hyperbolic metrics on a smooth product manifold R × S is not convex, even though it is path connected by means of piecewise convex combinations. [ABSTRACT FROM AUTHOR]